1. PLOT GRAPHICS

1. GRADIENT METHOD

   2.1. Constant step method

   2.2. Dynamic step method

1. Contour

1. CONTOUR AND SCATTER PLOT OF METHOD

   4.1. Contour and scatter plot for method with constant step

   4.2. Contour and scatter plot for method with dynamic step

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
import numpy as np
from IPython.display import display, Math, Latex
import pylab
import plot_methods
import optimization_methods
%matplotlib inline

Plot function graphic

my_function = lambda x, y: x**2+2*y**2+0.012*x*y-2*y+x

plot_methods.plot_function(my_function, 'My function')

Gradient descent

constant step

results_con_step = optimization_methods.gradient_descent_constant_step(my_function, [1,1], 1e-5, 0.001)

number of iteration: 2, current point: [0.99398205 0.99598408], function value: 1.9858626672233397
number of iteration: 3, current point: [0.99098213 0.99398822], function value: 1.9728967364860956
number of iteration: 4, current point: [0.98798824 0.99200038], function value: 1.9599987578859968
number of iteration: 5, current point: [0.98500036 0.99002052], function value: 1.9471683310148826
number of iteration: 6, current point: [0.98201848 0.98804862], function value: 1.9344050580935064
number of iteration: 7, current point: [0.97904259 0.98608464], function value: 1.9217085439530628
number of iteration: 8, current point: [0.97607267 0.98412855], function value: 1.9090783960163655
number of iteration: 9, current point: [0.97310871 0.98218032], function value: 1.896514224279188
number of iteration: 10, current point: [0.97015071 0.98023992], function value: 1.8840156412926525
number of iteration: 11, current point: [0.96719864 0.97830732], function value: 1.8715822621444627
number of iteration: 12, current point: [0.96425251 0.97638249], function value: 1.859213704441033
number of iteration: 13, current point: [0.96131229 0.97446539], function value: 1.8469095882896651
number of iteration: 14, current point: [0.95837797 0.97255599], function value: 1.8346695362807135
number of iteration: 15, current point: [0.95544954 0.97065426], function value: 1.822493173470089
number of iteration: 16, current point: [0.95252699 0.96876018], function value: 1.8103801273615332
number of iteration: 17, current point: [0.94961031 0.96687371], function value: 1.7983300278894752
number of iteration: 18, current point: [0.94669949 0.96499482], function value: 1.7863425074016113
number of iteration: 19, current point: [0.94379451 0.96312348], function value: 1.7744172006419623
number of iteration: 20, current point: [0.94089537 0.96125966], function value: 1.762553744733789
number of iteration: 21, current point: [0.93800204 0.95940333], function value: 1.7507517791628757
number of iteration: 22, current point: [0.93511452 0.95755446], function value: 1.7390109457606293
number of iteration: 23, current point: [0.9322328  0.95571302], function value: 1.727330888687562
number of iteration: 24, current point: [0.92935687 0.95387898], function value: 1.7157112544168367
number of iteration: 25, current point: [0.92648671 0.95205232], function value: 1.7041516917177884
number of iteration: 26, current point: [0.92362231 0.95023299], function value: 1.6926518516400129
number of iteration: 27, current point: [0.92076366 0.94842097], function value: 1.6812113874969614
number of iteration: 28, current point: [0.91791076 0.94661624], function value: 1.6698299548499507
number of iteration: 29, current point: [0.91506357 0.94481876], function value: 1.6585072114922714
number of iteration: 30, current point: [0.91222211 0.94302851], function value: 1.6472428174338387
number of iteration: 31, current point: [0.90938635 0.94124544], function value: 1.636036434884904
number of iteration: 32, current point: [0.90655628 0.93946955], function value: 1.62488772824124
number of iteration: 33, current point: [0.9037319  0.93770079], function value: 1.613796364068227
number of iteration: 34, current point: [0.90091318 0.93593915], function value: 1.602762011085626
number of iteration: 35, current point: [0.89810012 0.93418458], function value: 1.5917843401527003
number of iteration: 36, current point: [0.89529271 0.93243706], function value: 1.5808630242527038
number of iteration: 37, current point: [0.89249094 0.93069657], function value: 1.5699977384785364
number of iteration: 38, current point: [0.88969479 0.92896307], function value: 1.5591881600173707
number of iteration: 39, current point: [0.88690425 0.92723655], function value: 1.5484339681362207
number of iteration: 40, current point: [0.88411931 0.92551696], function value: 1.5377348441670855
number of iteration: 41, current point: [0.88133997 0.92380428], function value: 1.527090471492575
number of iteration: 42, current point: [0.8785662  0.92209849], function value: 1.5165005355316712
number of iteration: 43, current point: [0.87579801 0.92039955], function value: 1.5059647237251363
number of iteration: 44, current point: [0.87303536 0.91870744], function value: 1.4954827255216423
number of iteration: 45, current point: [0.87027827 0.91702214], function value: 1.485054232363313
number of iteration: 46, current point: [0.86752671 0.9153436 ], function value: 1.4746789376720075
number of iteration: 47, current point: [0.86478067 0.91367182], function value: 1.4643565368355569
number of iteration: 48, current point: [0.86204015 0.91200675], function value: 1.4540867271935451
number of iteration: 49, current point: [0.85930512 0.91034838], function value: 1.4438692080242364
number of iteration: 50, current point: [0.85657559 0.90869668], function value: 1.433703680530519
number of iteration: 51, current point: [0.85385153 0.90705161], function value: 1.4235898478265736
number of iteration: 52, current point: [0.85113294 0.90541316], function value: 1.4135274149246007
number of iteration: 53, current point: [0.84841981 0.90378129], function value: 1.403516088721665
number of iteration: 54, current point: [0.84571213 0.90215599], function value: 1.3935555779861515
number of iteration: 55, current point: [0.84300988 0.90053721], function value: 1.3836455933451446
number of iteration: 56, current point: [0.84031305 0.89892495], function value: 1.3737858472709994
number of iteration: 57, current point: [0.83762164 0.89731917], function value: 1.3639760540688175
number of iteration: 58, current point: [0.83493563 0.89571984], function value: 1.354215929863594
number of iteration: 59, current point: [0.83225501 0.89412694], function value: 1.344505192587207
number of iteration: 60, current point: [0.82957977 0.89254044], function value: 1.3348435619664243
number of iteration: 61, current point: [0.8269099  0.89096033], function value: 1.3252307595099082
number of iteration: 62, current point: [0.82424539 0.88938656], function value: 1.315666508495998
number of iteration: 63, current point: [0.82158622 0.88781913], function value: 1.3061505339604178
number of iteration: 64, current point: [0.8189324  0.88625799], function value: 1.2966825626838907
number of iteration: 65, current point: [0.8162839  0.88470313], function value: 1.2872623231801055
number of iteration: 66, current point: [0.81364071 0.88315452], function value: 1.2778895456838684
number of iteration: 67, current point: [0.81100283 0.88161214], function value: 1.26856396213888
number of iteration: 68, current point: [0.80837025 0.88007596], function value: 1.2592853061859657
number of iteration: 69, current point: [0.80574295 0.87854596], function value: 1.250053313151116
number of iteration: 70, current point: [0.80312092 0.8770221 ], function value: 1.2408677200340996
number of iteration: 71, current point: [0.80050415 0.87550438], function value: 1.231728265496777
number of iteration: 72, current point: [0.79789264 0.87399275], function value: 1.2226346898514264
number of iteration: 73, current point: [0.79528636 0.87248721], function value: 1.2135867350494043
number of iteration: 74, current point: [0.79268532 0.87098772], function value: 1.204584144669945
number of iteration: 75, current point: [0.7900895  0.86949425], function value: 1.1956266639084157
number of iteration: 76, current point: [0.78749889 0.8680068 ], function value: 1.1867140395657927
number of iteration: 77, current point: [0.78491347 0.86652532], function value: 1.1778460200369958
number of iteration: 78, current point: [0.78233325 0.8650498 ], function value: 1.1690223553003132
number of iteration: 79, current point: [0.7797582  0.86358021], function value: 1.1602427969059863
number of iteration: 80, current point: [0.77718832 0.86211653], function value: 1.1515070979658044
number of iteration: 81, current point: [0.7746236  0.86065874], function value: 1.142815013142163
number of iteration: 82, current point: [0.77206402 0.85920681], function value: 1.1341662986370586
number of iteration: 83, current point: [0.76950959 0.85776072], function value: 1.1255607121820623
number of iteration: 84, current point: [0.76696027 0.85632044], function value: 1.1169980130272532
number of iteration: 85, current point: [0.76441608 0.85488596], function value: 1.1084779619310887
number of iteration: 86, current point: [0.76187699 0.85345724], function value: 1.100000321149727
number of iteration: 87, current point: [0.75934299 0.85203427], function value: 1.0915648544270349
number of iteration: 88, current point: [0.75681408 0.85061702], function value: 1.0831713269840555
number of iteration: 89, current point: [0.75429024 0.84920547], function value: 1.0748195055092058
number of iteration: 90, current point: [0.75177147 0.8477996 ], function value: 1.066509158147761
number of iteration: 91, current point: [0.74925776 0.84639938], function value: 1.0582400544919937
number of iteration: 92, current point: [0.74674908 0.84500479], function value: 1.0500119655714892
number of iteration: 93, current point: [0.74424545 0.84361581], function value: 1.0418246638430693
number of iteration: 94, current point: [0.74174683 0.84223241], function value: 1.033677923180805
number of iteration: 95, current point: [0.73925323 0.84085458], function value: 1.0255715188666428
number of iteration: 96, current point: [0.73676464 0.83948229], function value: 1.0175052275806895
number of iteration: 97, current point: [0.73428103 0.83811552], function value: 1.0094788273913897
number of iteration: 98, current point: [0.73180241 0.83675425], function value: 1.001492097746257
number of iteration: 99, current point: [0.72932877 0.83539845], function value: 0.993544819462352
number of iteration: 100, current point: [0.72686008 0.8340481 ], function value: 0.9856367747170478
number of iteration: 101, current point: [0.72439636 0.83270319], function value: 0.9777677470383155
number of iteration: 102, current point: [0.72193757 0.83136368], function value: 0.9699375212960493
number of iteration: 103, current point: [0.71948372 0.83002957], function value: 0.9621458836924641
number of iteration: 104, current point: [0.71703479 0.82870081], function value: 0.9543926217531977
number of iteration: 105, current point: [0.71459078 0.82737741], function value: 0.9466775243182544
number of iteration: 106, current point: [0.71215167 0.82605932], function value: 0.9390003815329113
number of iteration: 107, current point: [0.70971745 0.82474654], function value: 0.9313609848391038
number of iteration: 108, current point: [0.70728812 0.82343904], function value: 0.9237591269662384
number of iteration: 109, current point: [0.70486366 0.82213679], function value: 0.9161946019226808
number of iteration: 110, current point: [0.70244407 0.82083979], function value: 0.9086672049869895
number of iteration: 111, current point: [0.70002933 0.819548  ], function value: 0.9011767326991775
number of iteration: 112, current point: [0.69761944 0.81826141], function value: 0.8937229828521389
number of iteration: 113, current point: [0.69521438 0.81697999], function value: 0.8863057544833299
number of iteration: 114, current point: [0.69281415 0.81570373], function value: 0.8789248478660376
number of iteration: 115, current point: [0.69041873 0.8144326 ], function value: 0.871580064501172
number of iteration: 116, current point: [0.68802812 0.81316658], function value: 0.864271207108851
number of iteration: 117, current point: [0.68564231 0.81190566], function value: 0.8569980796201737
number of iteration: 118, current point: [0.68326128 0.81064981], function value: 0.8497604871689435
number of iteration: 119, current point: [0.68088503 0.80939901], function value: 0.8425582360835941
number of iteration: 120, current point: [0.67851354 0.80815324], function value: 0.8353911338790221
number of iteration: 121, current point: [0.67614682 0.80691249], function value: 0.8282589892485206
number of iteration: 122, current point: [0.67378484 0.80567673], function value: 0.8211616120560092
number of iteration: 123, current point: [0.67142761 0.80444593], function value: 0.8140988133278781
number of iteration: 124, current point: [0.6690751  0.80322009], function value: 0.8070704052452502
number of iteration: 125, current point: [0.66672731 0.80199918], function value: 0.8000762011360829
number of iteration: 126, current point: [0.66438423 0.80078319], function value: 0.7931160154675683
number of iteration: 127, current point: [0.66204585 0.79957208], function value: 0.7861896638383166
number of iteration: 128, current point: [0.65971216 0.79836585], function value: 0.7792969629707187
number of iteration: 129, current point: [0.65738316 0.79716447], function value: 0.7724377307035155
number of iteration: 130, current point: [0.65505883 0.79596792], function value: 0.7656117859840306
number of iteration: 131, current point: [0.65273916 0.79477619], function value: 0.7588189488609378
number of iteration: 132, current point: [0.65042414 0.79358925], function value: 0.7520590404766645
number of iteration: 133, current point: [0.64811377 0.79240709], function value: 0.7453318830601712
number of iteration: 134, current point: [0.64580804 0.79122968], function value: 0.7386372999195376
number of iteration: 135, current point: [0.64350692 0.79005701], function value: 0.731975115434716
number of iteration: 136, current point: [0.64121043 0.78888906], function value: 0.7253451550504377
number of iteration: 137, current point: [0.63891854 0.78772581], function value: 0.7187472452688628
number of iteration: 138, current point: [0.63663125 0.78656724], function value: 0.7121812136426773
number of iteration: 139, current point: [0.63434855 0.78541333], function value: 0.7056468887679193
number of iteration: 140, current point: [0.63207043 0.78426407], function value: 0.6991441002770724
number of iteration: 141, current point: [0.62979688 0.78311943], function value: 0.6926726788320405
number of iteration: 142, current point: [0.62752789 0.78197939], function value: 0.6862324561171766
number of iteration: 143, current point: [0.62526345 0.78084395], function value: 0.6798232648327331
number of iteration: 144, current point: [0.62300355 0.77971307], function value: 0.6734449386877437
number of iteration: 145, current point: [0.62074819 0.77858674], function value: 0.6670973123934212
number of iteration: 146, current point: [0.61849735 0.77746494], function value: 0.660780221656361
number of iteration: 147, current point: [0.61625102 0.77634766], function value: 0.6544935031720684
number of iteration: 148, current point: [0.6140092  0.77523487], function value: 0.6482369946182305
number of iteration: 149, current point: [0.61177188 0.77412657], function value: 0.6420105346480862
number of iteration: 150, current point: [0.60953905 0.77302272], function value: 0.6358139628841282
number of iteration: 151, current point: [0.60731069 0.77192331], function value: 0.6296471199114244
number of iteration: 152, current point: [0.60508681 0.77082833], function value: 0.623509847271313
number of iteration: 153, current point: [0.60286739 0.76973776], function value: 0.6174019874551113
number of iteration: 154, current point: [0.60065242 0.76865157], function value: 0.6113233838975389
number of iteration: 155, current point: [0.59844189 0.76756976], function value: 0.6052738809706548
number of iteration: 156, current point: [0.59623579 0.7664923 ], function value: 0.5992533239775852
number of iteration: 157, current point: [0.59403412 0.76541917], function value: 0.593261559146353
number of iteration: 158, current point: [0.59183687 0.76435037], function value: 0.5872984336236313
number of iteration: 159, current point: [0.58964402 0.76328587], function value: 0.5813637954686952
number of iteration: 160, current point: [0.58745558 0.76222565], function value: 0.5754574936474066
number of iteration: 161, current point: [0.58527152 0.76116969], function value: 0.56957937802614
number of iteration: 162, current point: [0.58309184 0.76011799], function value: 0.5637292993659262
number of iteration: 163, current point: [0.58091654 0.75907052], function value: 0.5579071093163122
number of iteration: 164, current point: [0.57874559 0.75802727], function value: 0.5521126604097235
number of iteration: 165, current point: [0.57657901 0.75698822], function value: 0.5463458060554771
number of iteration: 166, current point: [0.57441676 0.75595334], function value: 0.5406064005339593
number of iteration: 167, current point: [0.57225886 0.75492264], function value: 0.5348942989908918
number of iteration: 168, current point: [0.57010528 0.75389608], function value: 0.5292093574317633
number of iteration: 169, current point: [0.56795603 0.75287366], function value: 0.5235514327159032
number of iteration: 170, current point: [0.56581108 0.75185535], function value: 0.5179203825510164
number of iteration: 171, current point: [0.56367043 0.75084113], function value: 0.5123160654875711
number of iteration: 172, current point: [0.56153408 0.74983101], function value: 0.5067383409130952
number of iteration: 173, current point: [0.55940202 0.74882494], function value: 0.5011870690469189
number of iteration: 174, current point: [0.55727423 0.74782293], function value: 0.49566211093444523
number of iteration: 175, current point: [0.55515071 0.74682495], function value: 0.49016332844188626
number of iteration: 176, current point: [0.55303144 0.74583099], function value: 0.48469058425074896
number of iteration: 177, current point: [0.55091643 0.74484103], function value: 0.4792437418525515
number of iteration: 178, current point: [0.54880566 0.74385505], function value: 0.4738226655434552
number of iteration: 179, current point: [0.54669912 0.74287305], function value: 0.46842722041895124
number of iteration: 180, current point: [0.54459681 0.741895  ], function value: 0.4630572723687576
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number of iteration: 182, current point: [0.54040482 0.73995069], function value: 0.45239333498939605
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number of iteration: 188, current point: [0.52792938 0.734211  ], function value: 0.4209997473723299
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number of iteration: 2759, current point: [-0.49702033  0.50148109], function value: -0.7529776898865721
number of iteration: 2760, current point: [-0.49703231  0.50148113], function value: -0.7529778331959002
number of iteration: 2761, current point: [-0.49704426  0.50148117], function value: -0.7529779759325809
number of iteration: 2762, current point: [-0.49705619  0.50148121], function value: -0.7529781180989021
number of iteration: 2763, current point: [-0.4970681   0.50148125], function value: -0.7529782596971434
number of iteration: 2764, current point: [-0.49707998  0.50148129], function value: -0.7529784007295743
number of iteration: 2765, current point: [-0.49709184  0.50148133], function value: -0.7529785411984561
number of iteration: 2766, current point: [-0.49710367  0.50148137], function value: -0.7529786811060403
number of iteration: 2767, current point: [-0.49711548  0.50148141], function value: -0.7529788204545702
number of iteration: 2768, current point: [-0.49712727  0.50148145], function value: -0.7529789592462794
number of iteration: 2769, current point: [-0.49713903  0.50148149], function value: -0.7529790974833932
number of iteration: 2770, current point: [-0.49715077  0.50148153], function value: -0.7529792351681275
number of iteration: 2771, current point: [-0.49716249  0.50148157], function value: -0.7529793723026896
number of iteration: 2772, current point: [-0.49717418  0.50148161], function value: -0.752979508889278
number of iteration: 2773, current point: [-0.49718585  0.50148165], function value: -0.7529796449300824
number of iteration: 2774, current point: [-0.49719749  0.50148169], function value: -0.7529797804272835
number of iteration: 2775, current point: [-0.49720912  0.50148173], function value: -0.7529799153830536
number of iteration: 2776, current point: [-0.49722072  0.50148177], function value: -0.7529800497995564
number of iteration: 2777, current point: [-0.49723229  0.50148181], function value: -0.7529801836789464
number of iteration: 2778, current point: [-0.49724385  0.50148185], function value: -0.7529803170233701
number of iteration: 2779, current point: [-0.49725538  0.50148189], function value: -0.7529804498349653
number of iteration: 2780, current point: [-0.49726688  0.50148193], function value: -0.7529805821158606
number of iteration: 2781, current point: [-0.49727837  0.50148197], function value: -0.7529807138681771
number of iteration: 2782, current point: [-0.49728983  0.501482  ], function value: -0.752980845094027
number of iteration: 2783, current point: [-0.49730127  0.50148204], function value: -0.7529809757955138
number of iteration: 2784, current point: [-0.49731268  0.50148208], function value: -0.7529811059747329
number of iteration: 2785, current point: [-0.49732407  0.50148212], function value: -0.7529812356337712
number of iteration: 2786, current point: [-0.49733544  0.50148216], function value: -0.7529813647747073
number of iteration: 2787, current point: [-0.49734679  0.5014822 ], function value: -0.7529814933996113
number of iteration: 2788, current point: [-0.49735811  0.50148224], function value: -0.7529816215105456
number of iteration: 2789, current point: [-0.49736942  0.50148228], function value: -0.7529817491095636
number of iteration: 2790, current point: [-0.4973807   0.50148232], function value: -0.752981876198711
number of iteration: 2791, current point: [-0.49739195  0.50148236], function value: -0.7529820027800254
number of iteration: 2792, current point: [-0.49740319  0.5014824 ], function value: -0.7529821288555357
number of iteration: 2793, current point: [-0.4974144   0.50148244], function value: -0.7529822544272634
number of iteration: 2794, current point: [-0.49742559  0.50148248], function value: -0.7529823794972214
number of iteration: 2795, current point: [-0.49743675  0.50148252], function value: -0.7529825040674145
number of iteration: 2796, current point: [-0.4974479   0.50148256], function value: -0.7529826281398401
number of iteration: 2797, current point: [-0.49745902  0.50148259], function value: -0.752982751716487
number of iteration: 2798, current point: [-0.49747012  0.50148263], function value: -0.7529828747993362
number of iteration: 2799, current point: [-0.4974812   0.50148267], function value: -0.7529829973903612
number of iteration: 2800, current point: [-0.49749225  0.50148271], function value: -0.752983119491527
number of iteration: 2801, current point: [-0.49750328  0.50148275], function value: -0.7529832411047913
number of iteration: 2802, current point: [-0.4975143   0.50148279], function value: -0.7529833622321035
number of iteration: 2803, current point: [-0.49752529  0.50148283], function value: -0.7529834828754054
number of iteration: 2804, current point: [-0.49753625  0.50148287], function value: -0.752983603036631
number of iteration: 2805, current point: [-0.4975472   0.50148291], function value: -0.752983722717707
number of iteration: 2806, current point: [-0.49755812  0.50148295], function value: -0.7529838419205518
number of iteration: 2807, current point: [-0.49756902  0.50148298], function value: -0.7529839606470761
number of iteration: 2808, current point: [-0.4975799   0.50148302], function value: -0.7529840788991838
number of iteration: 2809, current point: [-0.49759076  0.50148306], function value: -0.7529841966787699
number of iteration: 2810, current point: [-0.4976016  0.5014831], function value: -0.7529843139877234
number of iteration: 2811, current point: [-0.49761241  0.50148314], function value: -0.7529844308279241
number of iteration: 2812, current point: [-0.4976232   0.50148318], function value: -0.7529845472012454
number of iteration: 2813, current point: [-0.49763398  0.50148322], function value: -0.7529846631095531
number of iteration: 2814, current point: [-0.49764473  0.50148326], function value: -0.7529847785547052
number of iteration: 2815, current point: [-0.49765545  0.5014833 ], function value: -0.7529848935385525
number of iteration: 2816, current point: [-0.49766616  0.50148333], function value: -0.752985008062938
number of iteration: 2817, current point: [-0.49767685  0.50148337], function value: -0.7529851221296983
number of iteration: 2818, current point: [-0.49768751  0.50148341], function value: -0.7529852357406615
number of iteration: 2819, current point: [-0.49769815  0.50148345], function value: -0.7529853488976489
number of iteration: 2820, current point: [-0.49770877  0.50148349], function value: -0.7529854616024748
number of iteration: 2821, current point: [-0.49771938  0.50148353], function value: -0.7529855738569459
number of iteration: 2822, current point: [-0.49772995  0.50148357], function value: -0.7529856856628617
number of iteration: 2823, current point: [-0.49774051  0.5014836 ], function value: -0.7529857970220146
number of iteration: 2824, current point: [-0.49775105  0.50148364], function value: -0.7529859079361899
number of iteration: 2825, current point: [-0.49776156  0.50148368], function value: -0.7529860184071656
number of iteration: 2826, current point: [-0.49777206  0.50148372], function value: -0.7529861284367131
number of iteration: 2827, current point: [-0.49778253  0.50148376], function value: -0.7529862380265957
number of iteration: 2828, current point: [-0.49779299  0.5014838 ], function value: -0.7529863471785705
number of iteration: 2829, current point: [-0.49780342  0.50148383], function value: -0.7529864558943873
number of iteration: 2830, current point: [-0.49781383  0.50148387], function value: -0.752986564175789
number of iteration: 2831, current point: [-0.49782422  0.50148391], function value: -0.7529866720245116
number of iteration: 2832, current point: [-0.49783459  0.50148395], function value: -0.7529867794422839
number of iteration: 2833, current point: [-0.49784494  0.50148399], function value: -0.7529868864308276
number of iteration: 2834, current point: [-0.49785526  0.50148403], function value: -0.7529869929918583
number of iteration: 2835, current point: [-0.49786557  0.50148406], function value: -0.7529870991270844
number of iteration: 2836, current point: [-0.49787586  0.5014841 ], function value: -0.7529872048382069
number of iteration: 2837, current point: [-0.49788612  0.50148414], function value: -0.7529873101269209
number of iteration: 2838, current point: [-0.49789637  0.50148418], function value: -0.7529874149949141
number of iteration: 2839, current point: [-0.4979066   0.50148422], function value: -0.7529875194438677
number of iteration: 2840, current point: [-0.4979168   0.50148425], function value: -0.7529876234754561
number of iteration: 2841, current point: [-0.49792698  0.50148429], function value: -0.7529877270913472
number of iteration: 2842, current point: [-0.49793715  0.50148433], function value: -0.7529878302932018
number of iteration: 2843, current point: [-0.49794729  0.50148437], function value: -0.7529879330826746
number of iteration: 2844, current point: [-0.49795741  0.50148441], function value: -0.7529880354614134
number of iteration: 2845, current point: [-0.49796752  0.50148444], function value: -0.7529881374310591
number of iteration: 2846, current point: [-0.4979776   0.50148448], function value: -0.752988238993247
number of iteration: 2847, current point: [-0.49798766  0.50148452], function value: -0.7529883401496048
number of iteration: 2848, current point: [-0.49799771  0.50148456], function value: -0.7529884409017543
number of iteration: 2849, current point: [-0.49800773  0.50148459], function value: -0.7529885412513107
number of iteration: 2850, current point: [-0.49801773  0.50148463], function value: -0.7529886411998827
number of iteration: 2851, current point: [-0.49802771  0.50148467], function value: -0.7529887407490726
Precision: 9.982426344351942e-06

dynamic step

results_dyn_step = optimization_methods.gradient_descent(my_function, [1,1], 1e-5)

number of iteration: 2, current point: [-0.54205935 -0.02801692], function value: -0.19044503711757782
number of iteration: 3, current point: [-0.49881844  1.05669214], function value: -0.13651149009400831
number of iteration: 4, current point: [-0.50266956  0.48817176], function value: -0.752657727867009
number of iteration: 5, current point: [-0.50280241  0.50182808], function value: -0.753013307162182
number of iteration: 6, current point: [-0.50290919  0.50150074], function value: -0.7530135441436765
number of iteration: 7, current point: [-0.5030114  0.5015171], function value: -0.753013554108241
number of iteration: 8, current point: [-0.50300905  0.50150058], function value: -0.7530135541011796
number of iteration: 9, current point: [-0.50300902  0.50150923], function value: -0.7530135542438933
Precision: 8.652578261310483e-06

Contour

plot_methods.plot_contour(my_function, 'Contour')

Contour and Scatter

constant step contour

plot_methods.plot_contour_and_scatter_of_descent(my_function, results_con_step, 
                                                 'Contour and Scatter constant step')

dynamic step contour

plot_methods.plot_contour_and_scatter_of_descent(my_function, results_dyn_step, 
                                                 'Contour and Scatter dynamic step')